Disk read errors, especially with older disks can be a real problem. There are several reasons they occur and the good news is most can be resolved.
NOTE: This is from my trial & error process. Anything you choose to try is entirely at your own risk.
First things first. If you are reading/writing disks using my Arduino Reader/Writer design and you are NOT using an FTDI converter for reading OR writing disks (including on the UNO!) then this is the first thing you should change. See FTDI vs CH340 (and the Arduino UNO converter).
Secondly, if you are powering your drive from the USB port it may be getting insufficient power to run correctly. An external 5V (and possibly 12V) power supply should be added. Be sure to connect the GND from the external power supply to the GND used by the Arduino.
One of the major culprits of disk read errors is for the drive heads to become dirty. This can especially happen as a result of using old disks (see below).
There are two ways to clean the heads, you can either purchase and use a drive cleaning kit or disassemble the drive and clean the drive heads using a lint-free cloth and some isopropyl alcohol. You can also find several videos on YouTube showing you how to clean them manually.
It may sound strange, but disks that haven't been used in a while can develop mould on their surface. The sad part about this is when you put them in the drive the will make the heads dirty so you'll need to clean that too.
There are two methods for cleaning the mould off of a disk. The first is to physically open up the disk and clean them with lukewarm water etc as shown in this video.. This is quite drastic, but can work.
The second method is to clean the disk from the outside using something like this to hold the shutter open while you rotate the disk and clean it. You could again use water/soap, although if really needed you could also try isopropyl alcohol:
The MOST important thing about either method is to make sure the disk is completely dry before using it in the machine. With the second method especially, in interior of the disk can stay damp and can cause the disk not to spin properly, or worse damage the disk further.
In future, try to store your disks with a pack of silica gel just in case!
Some disks, especially the later ones were created using a cheaper process, and as such, some of these disks have started to deteriorate such that the physical surface of the disk is coming off.
Sadly these are probably unrecoverable so I would advise trying to grab off them what you can. They may make the drive head dirty, they might clean using the above approach, it just depends exactly how they have degraded. The chances are the drive head may wear away the surface that has the magnetic data in it.